2021 Pascal Problem 24

Yann writes down the first n consecutive positive integers, 1, 2, 3, 4, \ldots, n-1, n. He removes four different integers p, q, r,\ \text{s} from the list. At least three of p, q, r,\ \text{s} are consecutive and 100 < p < q < r < s. The average of the integers remaining in the list is 89.5625. The number of possible values of s is

*(The original version of this problem was missing the correct answer.)*

\textbf{(A)}\ 25\quad \textbf{(B)}\ 23\quad \textbf{(C)}\ 21\quad \textbf{(D)}\ 20\quad \textbf{(E)}\ 22

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.